1. Field of the Invention
The present invention relates to two-dimensional and three-dimensional polynucleic acid nanostructures which are periodic and thereby translationally symmetrical.
2. Description of The Related Art
A key aim of biotechnology and nanotechnology (Feynman et al, 1961, and Drexler, 1981) is a rational approach to the construction of new biomaterials, including individual geometrical objects and nanomechanical devices, and extended constructions, particularly periodic matter with control of the molecule architecture such that it would permit the fabrication of intricate arrangements of atoms to serve many practical purposes (Robinson et al, 1987; Seeman, 1991a; Seeman, 1991b). The informational macromolecules of biological systems, proteins and nucleic acids, are believed to have the potential to serve as building blocks for these constructions, because they are used for similar purposes in the cell. For instance, nanometer-scale circuitry and robotics could accomplish many tasks that are impossible today. One can envision improvements in the storage and retrieval of information, directed attacks on the molecular basis of medical problems, and the assembly of very smart materials as possible end products of the ability to control the structure of matter on the nanometer scale.
There are at least three key elements necessary for the control of three-dimensional structure in molecular construction that involves the high symmetry associated with crystals: (1) the predictable specificity of intermolecular interactions between components; (2) the structural predictability of intermolecular products; and (3) the structural rigidity of the components (Liu et al, 1994). DNA branched junctions are excellent building blocks from the standpoint of the first two requirements, which are also needed for the construction of individual objects, because (1) ligation directed by Watson-Crick base pairing between sticky-ended molecules has been used successfully to direct intermolecular specificity since the early 1970's (Cohen et al, 1973); and (2) the ligated product is double helical B-DNA, whose local structural parameters are well-known (Arnott et al, 1973).
The key problem in working with branched DNA as a construction medium is that branched junctions have been shown to be extremely flexible molecules (Ma et al, 1986; Petrillo et al, 1988). The ligation of 3-arm and 4-arm DNA branched junctions leads to many different cyclic products, suggesting that the angles between the arms of the junctions vary on the ligation time-scale; these angles are analogous to valence angles around individual atoms. Likewise, a 5-arm DNA branched junction has been shown to have no well-defined structure, and a 6-arm DNA branched junction has only a single preferred stacking domain (Wang et al, Biochem. 30:5667-5674). Leontis and his colleagues have shown that a three-arm branched junction containing a loop of two deoxythymidine nucleotides has a preferred stacking direction (Leontis et al, 1991) and ligation along this direction shows a lower propensity to cyclization (21.3%) than other directions (Liu et al, 1994), but it is not possible to treat the stacking domain in the Leontisian junction as a rigid component (Qi et al, 1996).
To overcome the problem of branched DNA being extremely flexible and therefore unsuitable from the standpoint of structural rigidity of the components as the third key element, DNA structures that fail to cyclize significantly in the course of ligation reactions (a measure of the rigidity of the DNA) were sought by the present inventors. DNA double crossover molecules, which are model systems for structures proposed to be involved in genetic recombination initiated by double strand breaks (Sun et al, 1991; Thaler et al, 22:169-197, 1988), as well as meiotic recombination (Schwacha et al, 1995), were explored with respect to the structural features of these molecules, and a laboratory of the inventors has shown that there are five different isomers of double crossover molecules (Fu et al, 1993). Double crossover molecules were used in the laboratory of the present inventor to establish the sign of the crossover node in the Holliday junction (Fu et al, 1994b), to construct symmetric immobile branched junctions (Zhang et al, 1994b), and to examine the effect of domain orientation on cleavage by the Holliday junction resolvase, endonuclease VII (Fu et al, 1994a). The helical domains were found to be parallel in three of the five isomers, and antiparallel in the other two. Those with parallel domains are not as well-behaved as those with antiparallel domains (Fu et al, 1993).
A laboratory of the present inventors reported the design of geometrical objects and lattices composed of rigid motifs, such as triangles and deltahedra, etc., formed from antiparallel nucleic acid double crossover molecules (Li et al, 1996; WO 97/41142). These findings stimulated a theoretical proposal to use aperiodic two-dimensional (2-D) lattices of double crossover molecules (Winfree, 1996) for DNA-based computation (Adleman, 1994). In the mathematical theory of tiling (Grunbaum et al, 1986), rectangular tiles with programmable interactions, known as Wang tiles, can be designed so that their assembly must mimic the operation of a chosen Turing Machine (H. Wang, 1963). Double crossover molecules acting as molecular Wang tiles could self-assemble to perform desired computations (Winfree, 1996).
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